Singer Asha Bhosle's 56-year-old daughter, Varsha, was found dead on a blood-soaked sofa in the Pedder Road flat she shared with her mother yesterday.
She had shot herself in her right temple with the licenced pistol of her younger brother.
No suicide note has been traced, but police are treating it as one.
Varsha had in the past tried to kill herself twice.
Asha Bhosle and other family members were in Singapore for an awards programme at the time of the incident.
She used a Belgian 0.6mm pistol to shoot herself in her right temple while sitting on the sofa.